Coach Lovie Smith said last Wednesday that Britt was out for personal reasons and he remained out all week. Britt also missed Sunday's game at Denver.
Asked Monday if Britt would be back this week, Smith said he didn't know. He didn't provide details on why Britt was out.
Britt, is in his eighth NFL season and second with the Texans, started 11 games last season. He started this year's opener against the Colts.
With Britt out, the Texans will again look to Scott Quessenberry to take his place.
The Texans on Tuesday also placed linebacker Kevin Pierre-Louis on the injured list after he sustained a groin injury against the Broncos.